The veteran reporter’s remarks on air that the Wimbledon winner was "never going to be a looker" sparked more than 600 complaints.

A BBC spokesman later apologised for the "insensitive" remark while Inverdale added: “Marion Bartoli is an incredible role model.”

However, Maria Miller has now written director general Lord Hall asking to be kept informed about "further action that is likely to be taken".

Aides said Mrs Miller met broadcasters a number of times over the last year to encourage them to improve coverage of women's sports.

She was moved to write the letter over the "derogatory" way Bartoli was treated during Wimbledon, one of the rare sporting events where women have a high media profile.

Mrs Miller wrote: "It is ... a matter of some concern to me that any comment on the looks and stature of a female athlete could be made in the context of one of the highlights of the UK's, and indeed the world's, sporting calendar.

'I am sure you will agree with me that it is vital that young women and girls in this country feel motivated both to take part in and to watch coverage of sport, and to know that they are included in the enjoyment of sport, and catered for by the media just as much as the male audience."

The Culture Secretary is also boycotting the Open over host Muirfield's refusal to admit female members and believes the problems with the two highlights of the sporting calendar are sending out the wrong message.

A government source said: "There are now one million more women playing sport as part of the Olympic legacy, which is fantastic.

"But despite this there are still national sporting events being held at clubs that refuse to allow women and BBC journalists referring to women in a sexist and derogatory fashion at a highlight of the British sporting calendar - the culture secretary is clear that this is a problem which can't be ignored."

Inverdale caused outrage with his comments about the Wimbledon winner on Radio 5 live shortly after she defeated Germany's Sabine Lisicki on Centre Court, telling listeners: "Do you think Bartoli's dad told her when she was little, 'You're never going to be a looker, you'll never be a Sharapova, so you have to be scrappy and fight'?"

His comments sparked outrage on Twitter where one user branded him a "sexist dinosaur" and another called for him to be stripped of his job.

Inverdale attempted to clarify the "ham-fisted" comment on the following day and said he had written to Bartoli to apologise for using a "clumsy phrase".

He said: "The point I was trying to make in a rather ham-fisted kind of way is that the public perception of tennis players is that they're all 6 feet-tall Amazonian athletes.

"Marion, who is the Wimbledon champion, bucks that trend, and she is a fantastic example to all young people that it's attitude, and will and determination together obviously with talent that in the end gets you to the top.

"I've apologised to Marion by letter if any offence was caused and I do hope that we can leave the matter there."